Abstract: The average distance problem asks to find a good way to approximate a high-dimensional object, represented as a measure, by a one-dimensional object. We will discuss two variants of the ...

When most people think of shapes, they imagine a triangle, a rectangle, or maybe even a fancier-sounding rhombus or trapezoid. But to mathematicians, shapes encompass a vast universe of surprising ...

There's a good explanation for the eight-foot pit in the center of the lab in Fronczak Hall, UB physicist Sambandamurthy Ganapathy tells a visitor from the Reporter. Slated for installation beneath ...

The notion of dimension at first seems intuitive. Glancing out the window we might see a crow sitting atop a cramped flagpole experiencing zero dimensions, a robin on a telephone wire constrained to ...

The fields of finite-element analysis, failure analysis, and solid mechanics all express stresses in terms of tensors. Engineering literature usually treats a tensor as a symbol dressed with indices ...

Mathematicians are “reinventing the wheel” by giving it a new shape. Their newly imagined wheel looks like a many-dimensional guitar pick, and it could theoretically roll in ways beyond our ...

Scheme illustration of object identification and all-optical 3D reconstruction system. (a) A contour surface image of the object can be obtained in a single processing of the system. (b) High-contrast ...